How long should it take a cut on my finger to heal? i cut it in the kitchen last week and it is still a bit tender and sore.

Weeks: It truly depends on the severity of the cut (superficial vs deep) and how much protection that site is recieving --> is it constantly being irritated or are you protecting it with a bandage. Furthermore, if it is draining pus and looks reddened/swollen, you may have an inflammatory reaction going on due to presence of bacteria. Keep the area clean, protect it and it should heal.

2 weeks for most: Keep it clean and prevent infection. The time it takes to heal depends on the location (crease) and depth. Usully 2 weeks.

Maximize healing: The real question is what not to do that slows down healing. Avoid using alcohol, peroxide, hibiclens, betadine, and bleach solutions. Inflammation ( red, hot, swollen, tender) is important to healing so anti-inflammatories (motrin, advil) are bad. Cover the area with a clean dressing changed every other day and protected from trauma. Antibiotics do not help healing unless it is truly infected.